Q. 3 H3.9( 7 Votes )

# Let’s find G.C.D of the following algebraic expression:

8(x^{2}-4),12(x^{3} + 8),36(x^{2}-3x-10)

Answer :

Factors of 8(x^{2}-4)=2×2×2×(x-2)×(x + 2)

Factors of 12(x^{3} + 8)

=2×2×3×(x + 2)×(x^{2}-2x + 4)

… ((x^{3} + 8)= (x + 2)×(x^{2}-2x + 4) from properties)

Factors of 36(x^{2}-3x-10)

Factors of (x^{2}-3x-10)

=(x^{2}-5x + 2x-10)

=x(x-5) + 2(x-5)

=(x + 2)(x-5)

Factors of 36(x^{2}-3x-10)=2×2×3×3×(x + 2)×(x-5)

GCD is the greatest common divisor, which is equal to the product of all the common divisors.

∴the GCD of 8(x^{2}-4),12(x^{3} + 8),36(x^{2}-3x-10) is 4(x + 2)

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